Question

$500 is invested at 5% interest compounded quarterly. How long will it take to equal $800? Round to the nearest tenth of a year. [Use A = P(1 + r/n)nt]

Answer 1

given:

a = $800

p = $500

r = 5% = 5/500 = 0.05

n = 4 (since we are compouding quarterly)

t = ?

using formular

a = p(1 + r/n)^nt

800 = 500(1 + 0.05/4)^4xt

500(1 + 0.05/4)^4t = 800

divide both sides by 500

500(1 + 0.05/4)^4t/500 = 800/500

(1 + 0.05/4)^4t = 8/5 [if f(x) = g (x) then ln(f(x)) = lin(g(x))

ln ((1 + 0.05/4)^4t) = ln(8/5) [ apply log rule : loga(x^b) = b . loga(x)

4t ln(1 + 0.05/4) = ln(8/5)

t = ln(8/5)/4ln(4.05/4)

t = 9.45

t = 9.5 years.